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    Probability, Confidence Interval & Hypothesis Testing

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    See attached file for 3 problems: Tesla Motors, PC manufacturer and large insurance company claims

    4. Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla's requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is MegaStat output from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer.

    Descriptive statistics

    count 16
    mean 99.938
    sample variance 2.313
    sample standard deviation 1.521
    minimum 97
    maximum 102.9
    range 5.9

    population variance 2.169
    population standard deviation 1.473

    standard error of the mean 0.380

    tolerance interval 95.45% lower 96.896
    tolerance interval 95.45% upper 102.979
    half-width 3.042

    1st quartile 98.900
    median 99.850
    3rd quartile 100.475
    interquartile range 1.575
    mode 98.900

    5. A PC manufacturer claims that no more than 5% of their machines are defective. In a random sample of 100 machines, it is found that 8.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacture's claim, and explain your answer..

    MegaStat Output
    Hypothesis test for proportion vs. hypothesized value

    Observed Hypothesized
    0.085 0.05 p (as decimal)
    9/100 5/100 p (as fraction)
    8.5 5.0 X
    100 100 n

    0.0218 std. error
    1.61 Z
    .0541 p-value (one-tailed, upper)

    6. The following table gives the number of claims at a large insurance company by kind and geographical region.
    East South
    Midwest
    West
    Totals

    Hospitalization
    102
    98
    39
    62
    301

    Physician's Visit
    263
    514
    120
    351
    1248

    Outpatient Treatment
    100
    226
    65
    99
    490

    Totals
    465
    838
    224
    512
    2039

    (A) Referring to the above table, if a bill is chosen at random, what is the probability that it is either from the East or from the West?
    (B) Referring to the above table, given that the bill is from the Midwest, what is the probability that it is for a Physician's Visit?

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    https://brainmass.com/statistics/hypothesis-testing/probability-confidence-interval-hypothesis-testing-337673

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    Solution Summary

    The solution provides step by step method for the calculation of confidence interval, hypothesis testing and probability. Formula for the calculation and Interpretations of the results are also included.

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